Zienkiewicz O.C., Taylor R.L. Vol. 3. The finite - tiera.ru

The modules are constructed essentially as in Chapter 20, Volume 1 starting with
(1) the data input module with preprocessing and continuing with (2) the solution
module and (3) the output module. However, unlike the generalized program of
Chapter 20, Volume 1, the program CBS¯ow only contains the listing for solving
transient Navier±Stokes (or Euler±Stokes) equations iteratively. Here there are
many possibilities such as fully explicit forms, semi-implicit forms, quasi-implicit
forms and fully implicit forms as discussed in Chapter 3 of this volume. We concentrate
mainly on the ®rst two forms which require small memory and simple solution
procedures compared to other forms.
In both the compressible and incompressible ¯ow codes, only non-dimensional
equations are used. The reader is referred to the appropriate chapters of this
volume (Chapters 3, 4 and 5) for di€erent non-dimensional parameters.
In Sec. 9.2 we shall describe the essential features of data input to the program.
Here either structured or unstructured meshes can be used to divide the problem
domain into ®nite elements. Section 9.3 explains how the steps of the CBS algorithm
are implemented. In that section, we brie¯y remark on the options available for shock
capturing, various methods of time stepping and di€erent procedures for equation
solving. In Sec. 9.4, the output generated by the program and postprocessing
procedures are considered. In the last section (Sec. 9.5) we shall consider the
possibility of further extension of CBS¯ow to other problems such as mass transfer,
turbulent ¯ow, etc.
9.2 The data input module
This part of the program is the starting point of the calculation where the input data
for the solution module are prepared. Here an appropriate input ®le is opened and the
data are read from it. Unlike in Chapter 20, Volume 1, we have no mesh generator
coupled with CBS¯ow. However an advancing front unstructured mesh generator
and some structured mesh generators are provided separately. By suitable coupling,
the reader can implement various adaptive procedures as discussed in Chapters 4 and
5. Either structured or unstructured mesh data can be given as input to the program.
The general program structure and many more details can be found in Chapter 20,
Volume 1.
9.2.1 Mesh data ± nodal coordinates and connectivity
The data input module 275
Once the nodal coordinates and connectivity of a ®nite element mesh are available
from a mesh generator, they are allotted to appropriate arrays (for a detailed description
on the mesh, numbering etc., see Chapter 20, Volume 1). Essentially the same
arrays as described in Chapter 20, Volume 1 are used here. The coordinates are
allotted to X…i; j† with i de®ning the appropriate cartesian coordinates x 1…i ˆ 1†
and x 2…i ˆ 2† and j de®ning the global node number. Similarly the connectivity is
allotted to an array IX…k; l†. Here k is the local node number and l is the global
element number. It should be noted that the material code normally used in heat
conduction and stress analysis is not necessary.